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Sets, Combinatorics, and Probability
Exercises 15−18 concern 3 people participating in a race, with each participant equally likely to either finish
the race or drop out of the race.
15. What is the size of the sample space?
16. What is the probability of exactly 1 participant finishing the race?
17. What is the probability of no one finishing the race?
18. What is the probability of at least 2 of the participants finishing the race?
Exercises 19−24 concern a single card drawn from a standard 52-card deck. A standard deck has 13 cards from
each of 4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through 10, jack, queen, king,
or ace. Each face value is a “kind” of card. The jack, queen, and king are “face cards.”
19. What is the probability of drawing a diamond?
20. What is the probability of drawing a queen?
21. What is the probability of drawing the queen of diamonds?
22. What is the probability of drawing a queen or a diamond?
23. What is the probability of drawing a black card?
24. What is the probability of drawing a card with a value less than 4 (aces count low)?
Exercises 25−36 concern 2-card hands from a standard 52-card deck. A standard deck has 13 cards from each of
4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through 10, jack, queen, king, or ace.
Each face value is a “kind” of card. The jack, queen, and king are “face cards.”
25. What is the size of the sample space?
26. What is the probability that both cards are the same suit?
27. What is the probability that neither card is a spade?
28. What is the probability that both cards are spades?
29. What is the probability that exactly 1 card is a spade?
30. What is the probability that at least 1 card is a spade?
31. What is the probability that both cards are face cards?
32. What is the probability that exactly 1 card is a face card?
33. What is the probability that both cards are spade face cards?
34. What is the probability that both cards are either face cards or spades?
35. How does the answer to Exercise 30 relate to the answers for Exercises 28 and 29?
36. How does the answer to Exercise 30 relate to the answer for Exercise 27?
Exercises 37−40 concern possible games in the Hoosier lottery, the Indiana state lottery.
37. In the Daily 3 game, three numbers between 0 and 9 will be drawn in succession (repetitions allowed).
The player marks three numbers on a game card and has a choice of how to play, straight (the player’s
numbers will match the three numbers drawn in exact order) or box (the player’s numbers will match the
three drawn in any order).
a. What is the size of the sample space?
b. What is the probability of a straight?
c. What is the probability of a box if 3 distinct numbers are drawn?
d. What is the probability of a box if 2 of the numbers drawn are the same?
Sets, Combinatorics, and Probability
Exercises 15−18 concern 3 people participating in a race, with each participant equally likely to either finish
the race or drop out of the race.
15. What is the size of the sample space?
16. What is the probability of exactly 1 participant finishing the race?
17. What is the probability of no one finishing the race?
18. What is the probability of at least 2 of the participants finishing the race?
Exercises 19−24 concern a single card drawn from a standard 52-card deck. A standard deck has 13 cards from
each of 4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through 10, jack, queen, king,
or ace. Each face value is a “kind” of card. The jack, queen, and king are “face cards.”
19. What is the probability of drawing a diamond?
20. What is the probability of drawing a queen?
21. What is the probability of drawing the queen of diamonds?
22. What is the probability of drawing a queen or a diamond?
23. What is the probability of drawing a black card?
24. What is the probability of drawing a card with a value less than 4 (aces count low)?
Exercises 25−36 concern 2-card hands from a standard 52-card deck. A standard deck has 13 cards from each of
4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through 10, jack, queen, king, or ace.
Each face value is a “kind” of card. The jack, queen, and king are “face cards.”
25. What is the size of the sample space?
26. What is the probability that both cards are the same suit?
27. What is the probability that neither card is a spade?
28. What is the probability that both cards are spades?
29. What is the probability that exactly 1 card is a spade?
30. What is the probability that at least 1 card is a spade?
31. What is the probability that both cards are face cards?
32. What is the probability that exactly 1 card is a face card?
33. What is the probability that both cards are spade face cards?
34. What is the probability that both cards are either face cards or spades?
35. How does the answer to Exercise 30 relate to the answers for Exercises 28 and 29?
36. How does the answer to Exercise 30 relate to the answer for Exercise 27?
Exercises 37−40 concern possible games in the Hoosier lottery, the Indiana state lottery.
37. In the Daily 3 game, three numbers between 0 and 9 will be drawn in succession (repetitions allowed).
The player marks three numbers on a game card and has a choice of how to play, straight (the player’s
numbers will match the three numbers drawn in exact order) or box (the player’s numbers will match the
three drawn in any order).
a. What is the size of the sample space?
b. What is the probability of a straight?
c. What is the probability of a box if 3 distinct numbers are drawn?
d. What is the probability of a box if 2 of the numbers drawn are the same?